Problem: Solve for $x$ and $y$ using elimination. ${-5x-y = -46}$ ${6x+y = 54}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-5x-y = -46}\thinspace$ to find $y$ ${-5}{(8)}{ - y = -46}$ $-40-y = -46$ $-40{+40} - y = -46{+40}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 8}$ into $\thinspace {6x+y = 54}\thinspace$ and get the same answer for $y$ : ${6}{(8)}{ + y = 54}$ ${y = 6}$